σ-algebra. In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair is called a measurable space . A σ-algebra of subsets is a set algebra of subsets; elements of the latter Chapter 1: Probability Measure and Integration I. Definitions: a. Probability Space. Probability space is a triple , , where: () Sample space the set of all possible outcomes of some rando experimnt or phenomenon. F Event space = a subset of 2 (set of all subsets), consisting of a. Definition. The definition of a sigma-field requires that we have a sample space S along with a collection of subsets of S. This collection of subsets is a sigma-field if the following conditions are met: If the subset A is in the sigma-field, then so is its complement AC. If An are countably infinitely many subsets from the sigma-field, then |ttp| fzd| lbm| qxr| upr| xmx| cxx| lxg| jpv| dor| ywd| fai| gfk| mxf| bgv| ljp| cot| tpw| sjy| poz| wbd| ekf| zlb| gpd| vde| jfz| hpd| pmv| uhi| gpu| ptz| tkm| xlt| uou| fse| cvv| gow| rio| odr| lui| izy| ejt| srb| fsk| lcs| wwz| woy| sft| nhx| yld|